Polarizable Drude Model with s-Type Gaussian or Slater Charge Density for General Molecular Mechanics Force Fields

TrIP─Transformer Interatomic Potential Predicts Realistic Energy Surface Using Physical Bias

Accurate interatomic energies and forces enable high-quality molecular dynamics simulations, torsion scans, potential energy surface mappings, and geometry optimizations. Machine learning algorithms have enabled rapid estimates of the energies and forces with high accuracy. Further development of machine learning algorithms holds promise for producing universal potentials that support many different atomic species. We present the Transformer Interatomic Potential (TrIP): a chemically sound potential based on the SE(3)-Transformer. TrIP's species-agnostic architecture, which uses continuous atomic representation and homogeneous graph convolutions, encourages parameter sharing between atomic species for more general representations of chemical environments, maintains a reasonable number of parameters, serves as a form of regularization, and is a step toward accurate universal interatomic potentials. TrIP achieves state-of-the-art accuracies on the COMP6 benchmark with an energy prediction of just 1.02 kcal/mol MAE. We introduce physical bias in the form of Ziegler-Biersack-Littmark-screened nuclear repulsion and constrained atomization energies. An energy scan of a water molecule demonstrates that these changes improve long- and near-range interactions compared to other neural network potentials. TrIP also demonstrates stability in molecular dynamics simulations, demonstrating reasonable exploration of Ramachandran space.

An Imbalance in the Force: The Need for Standardized Benchmarks for Molecular Simulation

Force fields (FFs) for molecular simulation have been under development for more than half a century. As with any predictive model, rigorous testing and comparisons of models critically depends on the availability of standardized data sets and benchmarks. While such benchmarks are rather common in the fields of quantum chemistry, this is not the case for empirical FFs. That is, few benchmarks are reused to evaluate FFs, and development teams rather use their own training and test sets. Here we present an overview of currently available tests and benchmarks for computational chemistry, focusing on organic compounds, including halogens and common ions, as FFs for these are the most common ones. We argue that many of the benchmark data sets from quantum chemistry can in fact be reused for evaluating FFs, but new gas phase data is still needed for compounds containing phosphorus and sulfur in different valence states. In addition, more nonequilibrium interaction energies and forces, as well as molecular properties such as electrostatic potentials around compounds, would be beneficial. For the condensed phases there is a large body of experimental data available, and tools to utilize these data in an automated fashion are under development. If FF developers, as well as researchers in artificial intelligence, would adopt a number of these data sets, it would become easier to compare the relative strengths and weaknesses of different models and to, eventually, restore the balance in the force.

Synthesis, substitution kinetics, DNA/BSA binding and cytotoxicity of tridentate N^E^N (E = NH, O, S) pyrazolyl palladium(II) complexes

The pincer complexes, [Pd(L₁)Cl]BF₄ (PdL₁), [Pd(L₂)Cl]BF₄ (PdL₂), [Pd(L₃)Cl]BF₄ (PdL₃), [Pd(L₄)Cl]BF₄ (PdL₄) were prepared by reacting the corresponding ligands, 2,6-bis[(1H-pyrazol-1-yl)methyl]pyridine (L₁), bis[2-(1H-pyrazol-1-yl)ethyl]amine (L₂), bis[2-(1H-pyrazol-1-yl)ethyl]ether (L₃), and bis[2-(1H-prazol-1-yl)ethyl]sulphide (L₄) with [PdCl₂(NCMe)]₂ in the presence NaBF₄. The solid-state structures of complexes PdL₁-PdL₄ confirmed a tridentate coordination mode, with one chloro ligand completing the coordination sphere to afford square-planar complexes. Chemical behaviour of the complexes in solution confirms their stability in both aqueous and DMSO stock media. The electrochemical properties of the compounds showed irreversible two-electron reduction process. Kinetic reactivity of Pd complexes with the biological nucleophiles viz, thiourea (Tu), L-methionine (L-Met) and guanosine 5'-diphosphate disodium salt (5'-GMP) followed the order: PdL₂ < PdL₃ < PdL₄, and PdL₂ < PdL₁. The kinetic reactivity is subject to the electronic effects of the spectator ligand(s), and the trend was supported by the DFT computed results. The palladium complexes PdL₁-PdL₄ bind to calf thymus (CT-DNA) via intercalation mode. In addition, the bovine serum albumin (BSA) showed good binding affinity to the complexes. The mode of quenching mechanism of the intrinsic fluorescence of CT-DNA and BSA by the complexes was found to be static. The order of interactions of the complexes with DNA and BSA was in tandem with the rate of substitution kinetics. The complexes, however, displayed relatively low cytotoxicity (IC₅₀ > 100 µM) when tested against the human cervical adenocarcinoma (HeLa) cell line and the transformed human lung fibroblast cell line (MRC-5 SV2).

Evaluating fast methods for static polarizabilities on extended conjugated oligomers

Given the importance of accurate polarizability calculations to many chemical applications, coupled with the need for efficiency when calculating the properties of sets of molecules or large oligomers, we present a benchmark study examining possible calculation methods for polarizable materials. We first investigate the accuracy of the additive model used in GFN2, a highly-efficient semi-empirical tight-binding method, and the D4 dispersion model, comparing its predicted additive polarizabilities to ωB97XD results for a subset of PubChemQC and a compiled benchmark set of molecules spanning polarizabilities from approximately 3 ų to 600 ų, with some compounds in the range of approximately 1200-1400 ų. Although we find additive GFN2 polarizabilities, and thus D4, to have large errors with polarizability calculations on large conjugated oligomers, it would appear an empirical quadratic correction can largely remedy this. We also compare the accuracy of DFT polarizability calculations run using basis sets of varying size and level of augmentation, determining that a non-augmented basis set may be used for large, highly polarizable species in conjunction with a linear correction factor to achieve accuracy extremely close to that of aug-cc-pVTZ.

Metallic Effects on p-Hydroxyphenyl Porphyrin Thin-Film-Based Planar Optical Waveguide Gas Sensor: Experimental and Computational Studies

Metal effects on the gas sensing behavior of metal complexes of 5,10,15,20-tetrakis(4-hydroxyphenyl)porphyrin (THPP) thin film was investigated in terms of detecting NO₂ gas by the planar optical waveguide. For this purpose, several THPP and metal complexes were synthesized with different central metal ions: Co(II), Ni(II), Cu(II), and Zn(II). Planar optical gas sensors were fabricated with the metalloporphyrins deposited on K⁺ ion-exchanged soda-lime glass substrate with the spin coating method serving as host matrices for gas interaction. All of the THPP complex’s films were fully characterized by UV-Vis, IR and XPS spectroscopy, and the laser light source wavelength was selected at 520 and 670 nm. The results of the planar optical waveguide sensor show that the Zn–THPP complex exhibits the strongest response with the lowest detectable gas concentration of NO₂ gas for both 520 nm and 670 nm. The Ni–THPP and Co–THPP complexes display good efficiency in the detection of NO₂, while, on the other hand, Cu–THPP shows a very low interaction with NO₂ gas, with only 50 ppm and 200 ppm detectable gas concentration for 520 nm and 670 nm, respectively. In addition, molecular dynamic simulations and quantum mechanical calculations were performed, proving to be coherent with the experimental results.

CLIFF: A component-based, machine-learned, intermolecular force field

Computation of intermolecular interactions is a challenge in drug discovery because accurate ab initio techniques are too computationally expensive to be routinely applied to drug-protein models. Classical force fields are more computationally feasible, and force fields designed to match symmetry adapted perturbation theory (SAPT) interaction energies can remain accurate in this context. Unfortunately, the application of such force fields is complicated by the laborious parameterization required for computations on new molecules. Here, we introduce the component-based machine-learned intermolecular force field (CLIFF), which combines accurate, physics-based equations for intermolecular interaction energies with machine-learning models to enable automatic parameterization. The CLIFF uses functional forms corresponding to electrostatic, exchange-repulsion, induction/polarization, and London dispersion components in SAPT. Molecule-independent parameters are fit with respect to SAPT2+(3)δMP2/aug-cc-pVTZ, and molecule-dependent atomic parameters (atomic widths, atomic multipoles, and Hirshfeld ratios) are obtained from machine learning models developed for C, N, O, H, S, F, Cl, and Br. The CLIFF achieves mean absolute errors (MAEs) no worse than 0.70 kcal mol^-1 in both total and component energies across a diverse dimer test set. For the side chain-side chain interaction database derived from protein fragments, the CLIFF produces total interaction energies with an MAE of 0.27 kcal mol^-1 with respect to reference data, outperforming similar and even more expensive methods. In applications to a set of model drug-protein interactions, the CLIFF is able to accurately rank-order ligand binding strengths and achieves less than 10% error with respect to SAPT reference values for most complexes.

Semi-automated Optimization of the CHARMM36 Lipid Force Field to Include Explicit Treatment of Long-Range Dispersion

The development of the CHARMM lipid force field (FF) can be traced back to the early 1990s with its current version denoted CHARMM36 (C36). The parametrization of C36 utilized high-level quantum mechanical data and free energy calculations of model compounds before parameters were manually adjusted to yield agreement with experimental properties of lipid bilayers. While such manual fine-tuning of FF parameters is based on intuition and trial-and-error, automated methods can identify beneficial modifications of the parameters via their sensitivities and thereby guide the optimization process. This work introduces a semi-automated approach to reparametrize the CHARMM lipid FF with consistent inclusion of long-range dispersion through the Lennard-Jones particle-mesh Ewald (LJ-PME) approach. The optimization method is based on thermodynamic reweighting with regularization with respect to the C36 set. Two independent optimizations with different topology restrictions are presented. Targets of the optimizations are primarily liquid crystalline phase properties of lipid bilayers and the compression isotherm of monolayers. Pair correlation functions between water and lipid functional groups in aqueous solution are also included to address headgroup hydration. While the physics of the reweighting strategy itself is well-understood, applying it to heterogeneous, complex anisotropic systems poses additional challenges. These were overcome through careful selection of target properties and reweighting settings allowing for the successful incorporation of the explicit treatment of long-range dispersion, and we denote the newly optimized lipid force field as C36/LJ-PME. The current implementation of the optimization protocol will facilitate the future development of the CHARMM and related lipid force fields.

Microscopic origins of conductivity in molten salts unraveled by computer simulations

Molten salts are crucial materials in energy applications, such as batteries, thermal energy storage systems or concentrated solar power plants. Still, the determination and interpretation of basic physico-chemical properties like ionic conductivity, mobilities and transference numbers cause debate. Here, we explore a method for determination of ionic electrical mobilities based on non-equilibrium computer simulations. Partial conductivities are then determined as a function of system composition and temperature from simulations of molten LiF_αCl_βI_γ (with α + β + γ = 1). High conductivity does not necessarily coincide with high Li⁺ mobility for molten LiF_αCl_βI_γ systems at a given temperature. In salt mixtures, the lighter anions on average drift along with Li⁺ towards the negative electrode when applying an electric field and only the heavier anions move towards the positive electrode. In conclusion, the microscopic origin of conductivity in molten salts is unraveled here based on accurate ionic electrical mobilities and an analysis of the local structure and kinetics of the materials.

Substituent Effect on Porphyrin Film-Gas Interaction by Optical Waveguide: Spectrum Analysis and Molecular Dynamic Simulation

Substituent effect on optical gas sensing performance in porphyrin-based optical waveguide detection system was studied by molecular dynamics simulation (MDS), absorption/emission spectrum analysis, and optical waveguide (OWG) detection. The affinities of porphyrin with seven types of substituents (-H, -OH, -tBu, -COOH, -NH2, -OCH3, -SO3-) on para position of meso-phenyl porphyrin toward gas molecules in adsorption process were studied in different size of boxes with the same pressure and concentration. Analyte gases (CO2, H2S, HCl, NO2) were exposed to porphyrin film in absorption spectrophotometer, and in OWG with evanescent field excited by a guiding laser light with 670 nm wavelength. The extent of interaction between host molecule and the guest analytes was analyzed by the number of gas molecules in vicinity of 0.3 nm around substituents of porphyrin molecules. Optical waveguide results reveal that sulfonate porphyrin is mostly responsive to hydrochloride, hydrosulfide gas and nitrogen dioxide gases with strong response intensity. Molecular dynamics and spectral analysis provide objective information about the molecular state and sensing properties. Molecular rearrangements induced by gas exposure was studied by spectral analysis and surface morphology before and after gas exposure taking hydrosulfide gas as an example. Film-gas interaction mechanism was discussed in terms of each gas and substituent group characters.

Systematic design of biomolecular force fields

Force fields for the study of biomolecules have been developed in a predominantly organic manner by regular updates over half a century. Together with better algorithms and advances in computer technology, force fields have improved to yield more robust predictions. However, there are also indications to suggest that intramolecular energy functions have not become better and that there still is room for improvement. In this review, systematic efforts toward development of novel force fields from scratch are described. This includes an estimate of the complexity of the problem and the prerequisites in the form of data and algorithms. It is suggested that in order to make progress, an effort is needed to standardize reference data and force field validation benchmarks.

Deriving a Polarizable Force Field for Biomolecular Building Blocks with Minimal Empirical Calibration

Force field parametrization involves a complex set of linked optimization problems, with the goal of describing complex molecular interactions by using simple classical potential-energy functions that model Coulomb interactions, dispersion, and exchange repulsion. These functions comprise a set of atomic (and molecular) parameters and together with the bonded terms they constitute the molecular mechanics force field. Traditionally, many of these parameters have been fitted in a calibration approach in which experimental measures for thermodynamic and other relevant properties of small-molecule compounds are used for fitting and validation. As these approaches are laborious and time-consuming and represent an underdetermined optimization problem, we study methods to fit and derive an increasing number of parameters directly from electronic structure calculations, in order to greatly reduce possible parameter space for the remaining free parameters. In the current work we investigate a polarizable model with a higher order dispersion term for use in biomolecular simulation. Results for 49 biochemically relevant molecules are presented including updated parameters for hydrocarbon side chains. We show that our recently presented set of QM/MM derived atomic polarizabilities can be used in direct conjunction with partial charges and a higher order dispersion model that are quantum-mechanically determined, to freeze nearly all (i.e., 132 out of 138) nonbonded parameters to their quantum determined values.

Rotational and Translational Diffusion of Proteins as a Function of Concentration

Atomistic simulations of three different proteins at different concentrations are performed to obtain insight into protein mobility as a function of protein concentration. We report on simulations of proteins from diluted to the physiological water concentration (about 70% of the mass). First, the viscosity was computed and found to increase by a factor of 7-9 going from pure water to the highest protein concentration, in excellent agreement with in vivo nuclear magnetic resonance results. At a physiological concentration of proteins, the translational diffusion is found to be slowed down to about 30% of the in vitro values. The slow-down of diffusion found here using atomistic models is slightly more than that of a hard sphere model that neglects the electrostatic interactions. Interestingly, rotational diffusion of proteins is slowed down somewhat more (by about 80-95% compared to in vitro values) than translational diffusion, in line with experimental findings and consistent with the increased viscosity. The finding that rotation is retarded more than translation is attributed to solvent-separated clustering. No direct interactions between the proteins are found, and the clustering can likely be attributed to dispersion interactions that are stronger between proteins than between protein and water. Based on these simulations, we can also conclude that the internal dynamics of the proteins in our study are affected only marginally under crowding conditions, and the proteins become somewhat more stable at higher concentrations. Simulations were performed using a force field that was tuned for dealing with crowding conditions by strengthening the protein-water interactions. This force field seems to lead to a reproducible partial unfolding of an α-helix in one of the proteins, an effect that was not observed in the unmodified force field.

Large scale relative protein ligand binding affinities using non-equilibrium alchemy

Ligand binding affinity calculations based on molecular dynamics (MD) simulations and non-physical (alchemical) thermodynamic cycles have shown great promise for structure-based drug design. However, their broad uptake and impact is held back by the notoriously complex setup of the calculations. Only a few tools other than the free energy perturbation approach by Schrödinger Inc. (referred to as FEP+) currently enable end-to-end application. Here, we present for the first time an approach based on the open-source software pmx that allows to easily set up and run alchemical calculations for diverse sets of small molecules using the GROMACS MD engine. The method relies on theoretically rigorous non-equilibrium thermodynamic integration (TI) foundations, and its flexibility allows calculations with multiple force fields. In this study, results from the Amber and Charmm force fields were combined to yield a consensus outcome performing on par with the commercial FEP+ approach. A large dataset of 482 perturbations from 13 different protein-ligand datasets led to an average unsigned error (AUE) of 3.64 ± 0.14 kJ mol-1, equivalent to Schrödinger's FEP+ AUE of 3.66 ± 0.14 kJ mol-1. For the first time, a setup is presented for overall high precision and high accuracy relative protein-ligand alchemical free energy calculations based on open-source software.

A collection of forcefield precursors for metal-organic frameworks

A host of important performance properties for metal-organic frameworks (MOFs) and other complex materials can be calculated by modeling statistical ensembles. The principle challenge is to develop accurate and computationally efficient interaction models for these simulations. Two major approaches are (i) ab initio molecular dynamics in which the interaction model is provided by an exchange-correlation theory (e.g., DFT + dispersion functional) and (ii) molecular mechanics in which the interaction model is a parameterized classical force field. The first approach requires further development to improve computational speed. The second approach requires further development to automate accurate forcefield parameterization. Because of the extreme chemical diversity across thousands of MOF structures, this problem is still mostly unsolved today. For example, here we show structures in the 2014 CoRE MOF database contain more than 8 thousand different atom types based on first and second neighbors. Our results showed that atom types based on both first and second neighbors adequately capture the chemical environment, but atom types based on only first neighbors do not. For 3056 MOFs, we used density functional theory (DFT) followed by DDEC6 atomic population analysis to extract a host of important forcefield precursors: partial atomic charges; atom-in-material (AIM) C6, C8, and C10 dispersion coefficients; AIM dipole and quadrupole moments; various AIM polarizabilities; quantum Drude oscillator parameters; AIM electron cloud parameters; etc. Electrostatic parameters were validated through comparisons to the DFT-computed electrostatic potential. These forcefield precursors should find widespread applications to developing MOF force fields.

Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields

Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.

Interactions of Water and Alkanes: Modifying Additive Force Fields to Account for Polarization Effects

Atomistic biomolecular simulations predominantly utilize additive force fields (FF), where the electrostatic potential is modeled by fixed point charges. Among other consequences, the lack of polarizability in these models undermines the balance of hydrophilic/hydrophobic nonbonded interactions. Simulations of water/alkane systems using the TIP3P water model and CHARMM36 parameters reveal a 1 kcal/mol overestimate of the experimental transfer free energy of water to hexadecane; more recent optimized water models (SPC/E, TIP4P/2005, TIP4P-Ew, TIP3P-FB, TIP4P-FB, OPC, TIP4P-D) overestimate this transfer free energy by approximately 2 kcal/mol. In contrast, the polarizable SWM4-NDP and SWM6 water models reproduce experimental values to within statistical error. As an alternative to explicitly modeling polarizability, this paper develops an efficient automated workflow to optimize pair-specific Lennard-Jones parameters within an additive FF. Water/hexadecane is used as a prototype and the free energy of water transfer to hexadecane as a target. The optimized model yields quantitative agreement with the experimental transfer free energy and improves the water/hexadecane interfacial tension by 6%. Simulations of five different lipid bilayers show a strong increase of water permeabilities compared to the unmodified CHARMM36 lipid FF which consistently improves match with experiment: the order-of-magnitude underestimate for monounsaturated bilayers is rectified and the factor of 2.8-4 underestimate for saturated bilayers is turned into a factor of 1.5-3 overestimate. While agreement with experiment is decreased for the diffusion constant of water in hexadecane, alkane transfer free energies, and the bilayers' area per lipid, the method provides a permeant-specific route to achieve a wide range of heterogeneous observables via rapidly optimized pairwise parameters.

Polarizable Force Fields for Biomolecular Simulations: Recent Advances and Applications

Realistic modeling of biomolecular systems requires an accurate treatment of electrostatics, including electronic polarization. Due to recent advances in physical models, simulation algorithms, and computing hardware, biomolecular simulations with advanced force fields at biologically relevant timescales are becoming increasingly promising. These advancements have not only led to new biophysical insights but also afforded opportunities to advance our understanding of fundamental intermolecular forces. This article describes the recent advances and applications, as well as future directions, of polarizable force fields in biomolecular simulations.

Molten alkali halides – temperature dependence of structure, dynamics and thermodynamics

Temperature-induced structural, dynamical and thermodynamic changes reveal novel insights into the mechanism and dynamics of ion transport in molten salts.